Circle Equations and Properties

The video tutorial reviews circle equations, covering both standard and general forms. It explains how to convert between these forms, find the center and radius, and graph circles. Several examples demonstrate these concepts, including using Desmos for graphing, completing the square, and verifying points on a circle. The tutorial emphasizes understanding the relationship between the equation's components and the circle's properties.

What is the standard form of a circle's equation?

• (x + h)^2 + (y + k)^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

• x^2 + y^2 = r^2

• x^2 + y^2 + ax + by + c = 0

In the standard form of a circle's equation, what do the variables h and k represent?

• The slope of the tangent

• The radius of the circle

• The coordinates of the center

• The x-intercept and y-intercept

How do you determine the radius from the standard form equation of a circle?

• It is the sum of h and k

• It is the coefficient of y

• It is the coefficient of x

• It is the square root of the constant term on the right side

Given a circle with center (0, 4) and radius 5, what is its equation?

• (x + 0)^2 + (y + 4)^2 = 25

• (x - 0)^2 + (y - 4)^2 = 5

• x^2 + y^2 = 5

• x^2 + (y - 4)^2 = 25

If a circle's equation is (x - 7)^2 + (y - 2)^2 = 12, what is the radius?

• Square root of 12

• 12

• 3.46

• 7

What is the center of a circle with the equation (x - 7)^2 + (y - 2)^2 = 12?

• (-2, -7)

• (-7, -2)

• (7, 2)

• (2, 7)

Which equation represents a circle with center (-4, 8) and radius 7?

• (x + 4)^2 + (y + 8)^2 = 49

• (x - 4)^2 + (y + 8)^2 = 49

• (x + 4)^2 + (y - 8)^2 = 49

• (x - 4)^2 + (y - 8)^2 = 49

How do you convert a general form equation of a circle to standard form?

• By differentiating

• By using the quadratic formula

• By completing the square

• By factoring

What is the center of the circle given by the equation x^2 + y^2 - 8x + 4y - 5 = 0?

• (-2, 4)

• (-4, 2)

• (4, -2)

• (2, -4)

What is the radius of the circle with the equation x^2 + y^2 - 8x + 4y - 5 = 0?

• 2

• 3

• 4

• 5